This is an IGCSE additional mathematics permutation combination problem which I can't understand. Can somebody explain how this is done? My teacher says the question is incomplete.

Question
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A box contains sweets of 6 different flavours. There are at least 2 sweets of each flavour. A girl selects 3 sweets from the box. Given that these 3 sweets are not all of the same flavour, calculate the number of different ways she can select her 3 sweets.

(Original post by Paing Thet)
This is an IGCSE additional mathematics permutation combination problem which I can't understand. Can somebody explain how this is done? My teacher says the question is incomplete.

Question
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A box contains sweets of 6 different flavours. There are at least 2 sweets of each flavour. A girl selects 3 sweets from the box. Given that these 3 sweets are not all of the same flavour, calculate the number of different ways she can select her 3 sweets.

The question is complete, but there is a typo in the answer you've put.

Since the three chosen sweets are not all of the same flavour, either she has chosen 3 different flavours, or she has chosen 2 different flavours.

If 3 different, then she is choosing 3 from 6, and we have 6C3 = 20.

If there are two different flavours, then there is one of one flavour and two of a different flavour.
The one has 6 choices of flavours and once chosen the two have five choices, making 6x5=30 possibilities.

(Original post by ghostwalker)
The question is complete, but there is a typo in the answer you've put.

Since the three chosen sweets are not all of the same flavour, either she has chosen 3 different flavours, or she has chosen 2 different flavours.

If 3 different, then she is choosing 3 from 6, and we have 6C3 = 20.

If there are two different flavours, then there is one of one flavour and two of a different flavour.
The one has 6 choices of flavours and once chosen the two have five choices, making 6x5=30 possibilities.